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Topic: UNEQUAL INTEGERS (Read 1497 times) |
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pcbouhid
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UNEQUAL INTEGERS
« on: Dec 12th, 2005, 5:47pm » |
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Find the minimum area in square meters of a triangle whose sides and altitudes, measured in meters, are six different integers.
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JocK
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Re: UNEQUAL INTEGERS
« Reply #1 on: Dec 13th, 2005, 8:14am » |
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Not sure how to do this in a clever way.
I just inspected the set of primitive integer Heronian scalene triangles of increasing size (up to longest edge 50), and checked for which ones twice the area divided by the edge lengths leads to rationals with small denominators. Multiplying by the greatest common denominator resulted in a minimum area 1050 (a triangle with edges 35, 75, 100, and heights 60, 28, 21).
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| « Last Edit: Dec 13th, 2005, 8:33am by JocK » |
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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pcbouhid
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Re: UNEQUAL INTEGERS
« Reply #2 on: Dec 13th, 2005, 9:39am » |
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Right on the spot!
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Christine
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Re: UNEQUAL INTEGERS
« Reply #3 on: Jul 4th, 2013, 11:55am » |
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I found some time ago a question that is part of problem:
what are the dimensions of the most scalene triangle?
What does it mean?
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